The preposition "by" in "I see by your file"

"By" is correct. Grammatically, with a substantive as an object, it forms an instrumental modifier. It meaning is contextual but is usually informs you of who did something and/or the way in which something was done or how the action of the verb was caused, e.g. "by the means of" or "by the use of" or "with the assistance of".

"It was broken by a man with a hammer."

To quote the famous song by The Bee Gees "Stayin' Alive".

Well, you can tell by the way I use my walk

I'm a woman's man, no time to talk ...

OED

by, preposition

General scheme of signification.

I. Of position in space: (1) Position or action near, including notions of comparison by juxtaposition; (2) Direction and vague localization.

II. Of motion in space: (1) Motion alongside, along, or over a course; (2) Motion up to; (3) Motion alongside and beyond, including notions of distance to reach, and of excess, short-coming, or inferiority.

III. Of time.

IV. Of mental or ideal proximity.

V. Of medium, means, instrumentality, agency.

VI. Of circumstance, condition, manner, cause.

VII. In phrases.

This usage of 'by' is commonly used, but there may be some restrictions on the pairings of verb and prepositional complement.

• I can tell by his frown that he's not going to agree readily.
• I can see by the character style that a Chinese person wrote it.
• You can see by the look in her eyes....
• You can see by the angle of the draws that it is much steeper than my photo makes it look.
• You can see by the poster what fantastic Featured Artists The Menace had on her show this month.
• I can see by the map you may be a bit secluded; is this true?

(From the internet; grammar / punctuation adjusted.)

This 'by' means 'by considering / taking careful note of'.

I've not been able to find the exact sense in a dictionary, but Macmillan has the following sense for 'from':

from 6b used for giving the reason for a judgment or opinion

• I can tell from your eyes you’re a good man.
• From what I hear, Mr. Marlow is not a man to be trusted.

The defining statement fits well for this sense of 'by', and 'by' may replace 'from' in the first example (but not the second).

The examples using 'by' above become less fully acceptable, at least to many Brits, towards the latter ones. These have (example 4) non-personally related concepts and (5 and 6) concrete sources of information. 'File' arguably comes into this category (though it might be argued to refer metonymically to 'the information contained in your file').

A venerable example of this usage of by is the famous quote from Macbeth

• By the pricking of my thumbs ... Something wicked this way comes.

The 'I can tell' is not hard to retrieve, the NP after 'by' contains an ing-word ... but it's essentially the same usage. And, referring to a discernable human phenomenon (as well as being written by You-know-who), acceptable across the board.

With diagrams, features in diagrams, posters, maps etc, 'from' is not so generally acceptable; 'from' is doubtless more idiomatic. 'In' would work well with files, letters, written articles and the like.